Document analysis of mathematical texts is a challenging problem even for born-digital documents in standard formats. We present alternative approaches addressing this problem in the context of PDF documents. One uses an OCR approach for character recognition together with a virtual link network for structural analysis. The other uses direct extraction of symbol information from the PDF file with a two stage parser to extract layout and expression structures. With reference to ground truth data, we compare the effectiveness and accuracy of the two techniques quantitatively with respect to character identification and structural analysis of mathematical expressions and qualitatively with respect to layout analysis.

We present an approach to extracting mathematical formulae directly from PDF documents. We exploit both the perfect character information as well as additional font and spacing information available from a PDF document to ensure a faithful recognition of mathematical expressions. The extracted information can be post-processed to produce suitable markup that can be re-inserted into the PDF documents in order to enable the handling of mathematical formulae by accessibility technology. Furthermore, we demonstrate how we recognise different types of mathematical objects, such as relations, operators, etc., without reference to predefined knowledge or dictionary lookup, using character clustering and interspace and character font information alone, all of which contributes to our goal of reconstructing the intended semantics of a formula from its presentation.

Classes of matrices are often presented with symbolic dimensions using a mixture of terms and ellipsis symbols to describe their internal structure. While working with such classes of matrices is everyday mathematical practice, it has little automated support. We describe an algebraic encoding of such matrices in terms of support functions and define the corresponding addition and multiplication algorithms. It is, however, non-trivial to retrieve the structural description of the matrix resulting from these operations. We therefore define an abstract matrix as an encoding of support function combinations that enables simple recovery of the structural properties. This allows us to define arithmetic algorithms for abstract matrices as extensions of those for support function combinations using a normalising term rewrite system.

We introduce a new data type of abstract matrices that allows the description of underspecified matrices containing ellipses and their use as templates for classes of concrete matrices. We present a series of algorithms that fully analyses the structure of abstract matrices and their representation and supports subsequent instantiation to concrete matrices.

The automatic interpretation of mathematical text structures has received only limited attention so far. While there has been work on the particularities of the character recognition of two dimensional formulas such as matrices in texts, very little has been done on exploiting their additional semantics in order to make them available for further processing. We present an algorithm that provides the interface between the recognition of matrix expressions and their concrete interpretation as mathematical objects. Given an underspecified matrix representation as they commonly appear in textbooks, containing ellipses and fill symbols, our algorithm extracts the semantic information contained. Matrices are interpreted as a collection of regions that can be interpolated with a particular term structure. The effectiveness of our algorithm can be demonstrated by its ability to derive concrete instances for the processed matrix representations in a symbolic computation system.

KCM (Knowledge Crunching Machine) is a high-performance back-end processor which, coupled to a UNIX* desk-top workstation, provides a powerful and user-friendly Prolog environment catering for both development and execution of significant Prolog applications. This paper gives a general overview of the architecture of KCM stressing some new features like a 64-bit tagged architecture, shallow backtracking and an original memory management unit. Some early benchmark results obtained on prototype machines are presented. They show that KCM, which runs at a peak speed of 833 Klips on list concatenation, compares favorably with other dedicated Prolog machines and available commercial systems running on fast general purpose processors.